Benoît Tuybens | Searcharxiv

arXiv2025

Numerical study of boson mixtures with multi-component continuous matrix product states

The continuous matrix product state (cMPS) ansatz is a promising numerical tool for studying quantum many-body systems in continuous space. Although it provides a clean framework that allows one to directly simulate continuous systems, the optimization of cMPS is known to be a very challenging task, especially in the case of multi-component systems. In this work, we have developed an improved optimization scheme for multi-component cMPS that enables simulations of bosonic quantum mixtures with substantially larger bond dimensions than previous works. We benchmark our method on the two-component Lieb-Liniger model, obtaining numerical results that agree well with analytical predictions. Our work paves the way for further numerical studies of quantum mixture systems using the cMPS ansatz.

cond-mat.quant-gas↗

arXiv2021

Variational optimization of continuous matrix product states

Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial dimension. Unlike the quantum spin case however, for which the density matrix renormalization group and related matrix product state algorithms provide robust algorithms for optimizing the variational states, the optimization of cMPS for systems with inhomogeneous external potentials has been problematic. We resolve this problem by constructing a piecewise linear parameterization of the underlying matrix-valued functions, which enables the calculation of the exact reduced density matrices everywhere in the system by high-order Taylor expansions. This turns the variational cMPS problem into a variational algorithm from which both the energy and its backwards derivative can be calculated exactly and at a cost that scales as the cube of the bond dimension. We illustrate this by finding ground states of interacting bosons in external potentials, and by calculating boundary or Casimir energy corrections of continuous many-body systems with open boundary conditions.

quant-ph↗